Molecular and quantitative genetic variation within and between populations of the declining grassland species Saxifraga granulata

Abstract Formerly common plant species are expected to be particularly susceptible to recent habitat fragmentation. We studied the population genetics of 19 recently fragmented Saxifraga granulata populations (max. distance 61 km) in Luxembourg and neighboring Germany using RAPD markers and a common garden experiment. We assessed (1) the relationships between plant fitness, quantitative genetic variation, molecular genetic variation, and population size; and (2) the relative importance of genetic drift and selection in shaping genetic variation. Molecular genetic diversity was high but did not correlate with population size, habitat conditions, or plant performance. Genetic differentiation was low (F ST = 0.079 ± 0.135), and there was no isolation by distance. Longevity, clonality, and the long‐lived seed bank of S. granulata may have prevented strong genetic erosion and genetic differentiation among populations. However, genetic distinctness increased with decreasing genetic diversity indicating that random genetic drift occurred in the studied populations. Quantitative and molecular genetic variations were correlated, and their differentiation (Q ST vs. F ST) among S. granulata populations was similar, suggesting that mainly random processes have shaped the quantitative genetic differentiation among populations. However, pairwise quantitative genetic distances increased with geographic and climatic distances, even when adjusted for molecular genetic distances, indicating diversifying selection. Our results indicate that long‐lived clonal species may be buffered at least temporarily against the negative effects of fragmentation. The relationship between quantitative genetic and geographic distance may be a more sensitive indicator of selection than Q ST–F ST differences.


| INTRODUC TI ON
The intensification of agricultural land use at the expense of traditional land management practices has caused a decline of semi-natural grasslands in Western Europe (Matthies, 2000;Poschlod et al., 2005), and many formerly common grassland species now occur in smaller and more isolated populations (Oostermeijer et al., 1996;Saunders, 1991). Fragmented populations are more strongly threatened by environmental and demographic stochasticity (Matthies et al., 2004;Young et al., 1996).

Fragmentation reduces gene flow and increases genetic drift
and inbreeding leading to a loss of genetic variability (genetic erosion, Aguilar et al., 2008;Ellstrand & Elam, 1993;Fischer & Matthies, 1998a;González et al., 2020;Honnay et al., 2007;Van Rossum et al., 2004;Young et al., 1996), a reduction in plant performance (Aguilar et al., 2019;Fischer & Matthies, 1998b;Kéry et al., 2000;Leimu et al., 2006), and a lower evolutionary potential of populations (Weber & Kolb, 2014;Willi et al., 2006). Population fragmentation tends to increase the differentiation among populations through reduced gene flow and genetic drift (Ellstrand & Elam, 1993;Willi et al., 2007). The sensitivity of a species to genetic erosion depends on life-history traits such as its longevity or clonal growth (Nybom, 2004;van der Meer & Jacquemyn, 2015), ploidy level (Frankham, 2010;van der Meer & Jacquemyn, 2015), breeding system (Aguilar et al., 2008;Leimu et al., 2006), the efficiency of gene flow between populations through seeds and pollen (Ghazoul, 2005), and the longevity of the seed bank (Honnay et al., 2008). Gene flow is often strongly restricted even within plant populations, because of short distance pollination and limited seed dispersal (Scheepens et al., 2012). This can lead to a pattern of isolation by distance within populations, where individuals that grow close to each other are more closely related than random pairs of individuals (Vekemans & Hardy, 2004), and to a reduction in effective population size.
The evolutionary potential of a population depends on the genetic variation of quantitative traits, which are often under selection (Leinonen et al., 2008;Mittell et al., 2015;Reed & Frankham, 2001;. However, the quantitative genetic variability in populations of fragmented species has been studied far less frequently than that of neutral molecular markers (Edwards, 2015;Kramer & Havens, 2009), although the two types of genetic variability are often not related (Reed & Frankham, 2001;Volis et al., 2016). Studying the evolutionary potential of a population to adapt to changing conditions is important in order to assess its chances to persist in the long term and to develop better conservation measures.
The comparison of genetic differentiation in quantitative traits (Q ST ) with that in neutral molecular genetic markers (F ST ) has been used to estimate the relative contributions of drift and selection to the overall genetic variation among populations (Merilä & Crnokrak, 2001). If Q ST is similar to F ST , drift is the major evolutionary force shaping the overall genetic differentiation among populations. If Q ST is larger or smaller than F ST , divergent or stabilizing selection is contributing to the overall genetic variation among populations (Volis et al., 2005;. In most studies, Q ST was larger than F ST indicating that divergent selection is common in plant populations (e.g., meta-analyses by Leinonen et al., 2008;De Kort et al., 2013;. However, studies on common or recently fragmented grassland species have obtained conflicting results. In a study of Scabiosa columbaria in calcareous grasslands in the Swiss Jura (Scheepens et al., 2010), unifying selection was detected, while in a study in a small geographic area in Sweden, the same species showed signs of divergent selection (Waldmann & Andersson, 1998). In highly fragmented temperate grasslands of Australia, Rutidosis leptorrhynchoides showed divergent selection along environmental gradients (Pickup et al., 2012).
We studied the molecular and quantitative genetic variation within and among populations of the grassland species Saxifraga granulata ( Figure 1) in Luxembourg and a neighboring area in Germany to investigate the effects of the recent fragmentation on its populations. S. granulata is a formerly common grassland species that has strongly declined in the last decades and is now threatened in several European regions (Metzing et al., 2018;van der Meer & Jacquemyn, 2015;Walisch et al., 2012). A recent genetic study of S. granulata along two rivers in central Belgium found that populations had maintained high molecular genetic diversity despite increasing fragmentation (van der Meer & Jacquemyn, 2015). Our study was conducted in a different habitat, mesic grasslands, and extends the study by including quantitative genetic variation. We addressed the following questions: (1) Are there positive correlations between the performance of plants, quantitative genetic variation, molecular genetic variation, and population size? (2) Are molecular and quantitative genetic differentiation between populations related to geographical distance, and what is the relative importance of selection and drift for genetic differentiation? F I G U R E 1 Saxifraga granulata L.

| Study species
Saxifraga granulata L. is a perennial herb that is propagated both sexually by seeds and vegetatively by small bulbils produced at the base of the plant (Kaplan, 1995;Stroh, 2015). The seeds are very small (c. 0.5 × 0.3 mm, c. 40 μg) and dispersed by wind. Seedling establishment in the field is very low, and the main means of propagation is thought to be via bulbils (Richards, 1986). The above-ground parts wither over summer, and a new basal rosette is produced in autumn, which overwinters and may flower the next spring. The flowers of S. granulata are protandrous, but self-compatible (Hansen & Molau, 1994;Walisch et al., 2012). Pollination is assured by a wide range of insect species including flies and solitary bees (Hansen & Molau, 1994).
Geitonogamous selfing within the same genet is common. A pollination study in a large population of S. granulata in Luxembourg found a mixed mating system with an estimated selfing rate of 55% (Walisch et al., 2012). Saxifraga granulata occurs in mesic to dry grasslands across northern, western, and central Europe reaching its southern range limit in North Africa (Stroh, 2015). However, populations have declined over the past decades in many parts of its range (Metzing et al., 2018, van der Meer & Jacquemyn, 2015 due to changes in agricultural practices, such as the increased fertilization of meadows, the conversion of grasslands into arable fields (Walisch et al., 2012), and the use of broad-spectrum herbicides (Stroh, 2015).

| Study sites and collection of samples
In May and June 2002, we selected 15 sites in Luxembourg and four additional ones in the neighboring state of Rheinland-Pfalz in Germany for a study of the genetic structure of the populations (Table 1). The geographical distance between the sites ranged from 0.05 to 61 km (median: 11). The longitude and latitude of the center of each population were determined with a GPS, and population size was estimated as the number of flowering individuals. For each site, we obtained the bioclimatic variables mean diurnal temperature range, mean annual temperature, temperature seasonality (SD), minimum temperature of the coldest month, maximum temperature of the warmest month, temperature annual range, annual precipitation, precipitation seasonality (CV), precipitation of the wettest month, and precipitation of the driest month at a grid size of about 1 km 2 (30 arc s) from the Worldclim database version 1.4. (Hijmans et al., 2005). A principal component analysis of climate variables identified two principal components, which explained 93.5% of the total variation. PRECIP explained 76% and correlated strongly with annual precipitation (r = .97), precipitation of the driest (r = .92) and

| Cultivation of plants
In September 2009, we placed two batches of 15 seeds per mother plant in separate Petri dishes on moist filter paper and stratified them in a growth chamber at 4°C for 4 weeks. The temperature was raised to 20°C at the end of October, and the seeds were put under a 12 h day/12 h night light regime. The position of the Petri dishes was randomized every 3-4 days. Seed germination was recorded every 2 weeks, and 3-10 seedlings per mother plant (hereafter referred to as a seed family) of a minimum size of 1 cm were selected at random and planted into soaked peat pellets ("Jiffy pots"). The

| RAPD-PCR
The frozen dried leaf material was ground (Retsch MM200, In a first series of amplifications 60 10-base primers (Kits A, B, C from Operon Technologies) were screened in a random sequence and tested for reproducibility of the amplified fragment profile using four replicates of a single DNA extract. The first seven primers yielding good-quality reproducible patterns (primers A4, A7, A11, C1, C2, C6, C8) were selected for the RAPD analysis of 250 sampled plants (Table 2). Presence or absence of reliable bands on amplification products was scored visually using the program Quantity/One (Bio-Rad Laboratories), which were treated as phenotypes, with each band position representing a character either present or absent.
The final presence-absence matrix contained scores at 54 polymorphic band positions for all samples in the study. We replicated 356 combinations of DNA samples and markers after DNA extraction to estimate the error rate of the RAPD genotyping resulting in 2771 repeated banding scores (corresponding to 20.5% of the total dataset).
The second scoring was done by the same technician as the first one, and the error rate was estimated to be 6.6%. Because of the error rate of 6.6%, we considered plants differing by up to 3.6 (rounded to 4) loci as putative clones belonging to the same genotype (Ehrich et al., 2008). We only kept one randomly chosen putative clone per genotype in the RAPD matrix resulting in 247 samples used for further analysis.
We identified markers under divergent or balancing selection with the program BAYESCAN 2.1 with the false discovery rate set to 0.05 (see .

TA B L E 2 RAPD primers used
Primer Sequence 3 | DATA ANALYS IS

| Molecular genetic diversity within populations and structure among populations
To estimate allele frequencies, we used the Bayesian method with nonuniform prior distribution of allele frequencies (Zhivotovsky, 1999) as implemented in AFLP-SURV version 1.0 (Vekemans, 2002) with an estimate of Wright's inbreeding coefficient over all populations (F IS ). F IS was calculated using the approximate Bayesian computation for F-statistics (ABC4F) for dominant data . Genetic diversity within populations was calculated as (1)  and among individuals within populations was investigated by analysis of molecular variance (AMOVA) using GenAlex version 6.501 (Peakall & Smouse, 2006, see Excoffier et al., 1992, Stewart & Excoffier, 1996. We also calculated the mean genetic distance between each population and all other populations (mean pairwise F ST ) and related it to the genetic diversity of the populations to test whether genetic drift might have simultaneously resulted in increased distinctness of populations and reduced genetic diversity (see Yakimowski & Eckert, 2008).

| Within and between population quantitative genetic variation
We analyzed the effects of population and family nested within population on the measured plant traits. To obtain estimates of be-  (Walisch et al., 2012). We inferred that 55% of offspring originated from selfing in our study populations and assumed that the remaining 45% of offspring were full-sibs to obtain a weighted mean value of 0.3875 for θ. Q ST was hence calculated as We calculated mean CV genetic of all traits over the populations and tested whether they were significantly different from 0 using one sample t-tests. We used simple regressions to explore the relationship between the evolvability (CV genetic ) of each trait in a population and its heritability (h 2 ) and its population mean value. We estimated the overall quantitative genetic variability as the mean evolvability over all traits and studied the relation between mean evolvability and expected heterozygosity, PPL, mean heritability of the quantitative traits, and population size with simple regressions.
We also analyzed the relationship between population mean trait values and heritability.
We tested the relationship between pairwise molecular genetic  (Table 1). Molecular genetic diversity increased with population size, but the relationship was weak and not significant (r = .32, p = .18, Figure 2).
The AMOVA analysis showed that 11% of the variation was among populations (p < .001), while variation among individuals within populations accounted for 89%. F ST estimated by AFLP-SURV (assuming F IS = 0.643) was 0.079 ± 0.1348. The mean F ST between a population and all other populations was negatively related to its genetic diversity, i.e., the lower the molecular genetic diversity of a population was, the more distinct was it (r = −.72, p < .001; Figure 3).

| Population performance and quantitative genetic variation
There was no significant relationship between the various measures of performance in the common garden and the size of the population of origin or its molecular genetic diversity ( Table 3). The mean number of flowers produced per plant in the common garden and in the population of origin was only very weakly correlated (r = .14, p = .56).
Mean quantitative genetic diversity within populations estimated as evolvability (CV genetic ) was significantly larger than zero for plant diameter (t 18 = 12.7, p < .001), leaf width (t 18 = 9.9, p < .001), and number of flowers (t 18 = 11.5, p < .001; Figure 4). Mean evolvability averaged over the studied traits in a population varied from 9% to 31%. Evolvability and heritability (h 2 ) of the individual traits per population were strongly correlated (all r > .87, all p < .001), and mean evolvability and mean heritability averaged over all studied traits were also strongly correlated (r = .89, p < .001).
There was a strong positive relationship between the mean evolvability over all traits and H eN (r = .71, p < .001; Figure

| Genetic diversity of populations and plant performance
The overall molecular genetic diversity H eN of the populations of about only a third of that estimated by microsatellite marker studies (Nybom, 2004), the genetic diversity of our study populations was higher than the genetic diversity of riparian S. granulata populations in Belgium (H s = 0.68) estimated by microsatellite markers (van der Meer & Jacquemyn, 2015). In contrast to many other studies, we did not find reduced genetic diversity in small populations as a sign of drift (Aguilar et al., 2019;Fischer & Matthies, 1998a;Leimu et al., 2006). The recent fragmentation of their habitats due to the intensification of agriculture in the last decades has thus apparently not yet affected the genetic diversity of small S. granulata populations. A recent meta-analysis found in general negative effects of fragmentation on the genetic diversity of populations isolated for more than 50 years, but not for those isolated more recently (Schlaepfer et al., 2018). Similar to S. granulata, several other perennial long-lived species of European grasslands also showed a lack of a correlation between population size and genetic diversity, including Scabiosa columbaria (Waldmann & Andersson, 1998), Primula veris, Dianthus carthusianorum, Medicago falcata, Polygala comosa, and Salvia pratensis (Reisch et al., 2017). The long-lived seed bank (Milberg, 1992) and the longevity and clonality of the S. granulata plants may have buffered populations against genetic erosion (Nybom, 2004;van der Meer & Jacquemyn, 2015). A further reason for the high overall genetic diversity of S. granulata could be its polyploidy. As polyploidy plants contain more copies of the genome, they have a higher potential for mutations, and they are less prone to drift than diploids (Meirmans & Van Tienderen, 2013;van der Meer & Jacquemyn, 2015).
Inbreeding has very strong negative effects on the performance of S. granulata (Walisch et al., 2012). However, we found no relationship between plant performance in a common garden and the molecular genetic diversity or size of the population of origin, indicating no inbreeding depression in small populations. This is in contrast to the negative effects of fragmentation on the performance of other grassland plants (Bowman et al., 2008;Busch & Reisch, 2005;Fischer & Matthies, 1998b;Kéry et al., 2000;Schleuning et al., 2009;Vergeer et al., 2003). The lack of a relation between plant performance and molecular genetic diversity in the study populations could be due to the lack of genetic erosion in small populations, which restricted the range of genetic diversity observed (0.29-0.38).

| Molecular genetic variation between populations
The level of differentiation between the fragmented S. granulata populations was low (F ST = 0.11) and was much lower than the mean Φ ST found in studies of species with a similar life history using dominant markers (mixed mating species Φ ST = 0.40, long-lived species Φ ST = 0.25; Nybom, 2004). Our F ST value was also lower than the Φ ST values obtained in other studies at a similar geographical scale (e.g., Allnutt et al., 1999;Colling et al., 2010;Kuss et al., 2008;Müller et al., 2012;Tollefsrud et al., 1998). as F ST tends to increase with the distance between populations (Crispo & Hendry, 2005;Garnier et al., 2004;Kuss et al., 2008;Nybom, 2004). In contrast, current gene flow between populations is unlikely to have contributed to the low differentiation, because

TA B L E 3
Correlations between various performance measures of Saxifraga granulata plants raised in the common garden and the size and molecular genetic diversity of their population of origin. . However, in that study the maximum genetic distance between populations was much higher, in spite of similar maximum geographic distances. Moreover, in contrast to our study, the Belgian populations showed a pattern of IBD in both studied river systems, indicating moderate gene flow between populations, particularly between those that are close to each other (van der Meer & Jacquemyn, 2015). The lack of IBD in our study could be due to more extensive gene flow in the past unrelated to distance in the study region.

F I G U R E 4 Evolvability of performance traits of
Although mean F ST in S. granulata was relatively low, we found also signs of genetic drift, as the mean genetic distance between a population and all other populations (distinctness) was negatively related to its genetic diversity, indicating that the higher the loss of genetic diversity through drift was, the more distinct became a population. A similar relationship has been found in Vaccinium stamineum (Yakimowski & Eckert, 2008), Saxifraga sponhemica , and Gladiolus palustris (Daco et al., 2019).

| Quantitative genetic variation
Quantitative genetic diversity as measured by mean evolvability or heritability of the studied traits was not affected by population size, F I G U R E 5 Relationship between (a) mean evolvability and (b) mean heritability of the measured quantitative traits in a population and its molecular genetic diversity (Nei's gene diversity). We found a positive relation between the evolvability and the heritability (h 2 ) of each trait and averaged over all studied traits in a population, which is in contrast to the general conclusions of reviews by Houlé (1992) and Hansen et al. (2011) that evolvability and heritability are generally not correlated. Genetic variation of leaf width and plant diameter was negatively correlated with their population means observed in the common garden, indicating that the genetic variation in growth traits has been much reduced in populations where there has been strong selection for fast growth. This is in line with quantitative genetic theory that the selection of a fitter larger phenotype due to selection may go hand in hand with a loss of quantitative genetic variability within populations (Bulmer, 1971;Visscher et al., 2008).
Quantitative genetic variation of the populations of S. granulata measured as both evolvability and heritability was significantly correlated with molecular genetic diversity, in contrast to the results of many other studies (see review of Leinonen et al., 2008;Mittell et al., 2015;Reed & Frankham, 2001;, but see Toczydlowski & Waller, 2021). Both strong divergent and stabilizing selection will reduce the correlation between quantitative and molecular genetic variation, which is thus usually very low (Reed & Frankham, 2003). In contrast, the observed correlation in S. granulata indicated that there was no general strong effect of stabilizing or divergent selection on quantitative genetic variation.
Differentiation in quantitative genetic traits among populations of S. granulata as measured by Q ST was similar to that in molecular genetic variation as indicated by F ST and thus provided no evidence for an effect of selection on differentiation in quantitative traits (Merilä & Crnokrak, 2001). This is in contrast to the results of most quantitative genetic studies, which reported divergent selection (De Kort et al., 2013;Leinonen et al., 2008Leinonen et al., , 2013Merilä & Crnokrak, 2001).
The studied populations originated from a relatively small region and have similar habitats with limited variation of local environmental conditions, which have not resulted in an increase in mean quantitative genetic variation over the level expected by drift. However, in contrast to differentiation in neutral molecular genetic markers, differentiation in quantitative genetic variation increased with geographic distance in S. granulata, even when the potential effects of drift were controlled for, indicating divergent selection. Part of the relationship between quantitative genetic differentiation and geographic distance could be explained by increasing differences in climate, suggesting adaptation of the populations of S. granulata to local climatic conditions. However, after adjusting for the effects of climatic distance, quantitative genetic differentiation still increased with geographic distance indicating that differences in other environmental factors that increase with geographic distance, e.g., soil conditions, have also contributed to genetic differences between populations.

| CON CLUS IONS
The populations of S. granulata in the study area have been fragmented in the last decades, but the low overall genetic differentiation between populations, the similar levels of genetic variation in small and large populations, and the lack of evidence for a reduced fitness of plants from small populations due to drift load indicate that this formerly common species has not yet suffered from the fragmentation of its habitat. Strong genetic drift and the consequent loss of genetic diversity may have been prevented by polyploidy a long-lived seed bank and longevity of genets due to the production of vegetatively produced bulbils. Clonal growth makes genets potentially immortal and represents a potent buffer against the loss of diversity in populations (Eriksson, 1993;Watkinson & White, 1986).
However, we also found signs of genetic drift, and extant popula-

ACK N OWLED G M ENTS
We are grateful to the Station biologique de l'Ouest for sharing their map of extensively managed meadows in Luxembourg, to Corinne Steinbach for pointing out populations of Saxifraga granulata in Germany and for assistance in the field, and to Charel Conrardy and Manuel Kunsch for assistance with measurements in the common garden. Open Access funding enabled and organized by Projekt DEAL.

O PEN R E S E A RCH BA D G E S
This article has earned an Open Data badge for making publicly available the digitally-shareable data necessary to reproduce the reported results. The data is available at [https://doi.org/10.5061/ dryad.b8gth t7g5].

DATA AVA I L A B I L I T Y S TAT E M E N T
Individual genotype and common garden data as well as population level data are available at https://doi.org/10.5061/dryad.b8gth t7g5.